MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Hypothesis Testing for Frequency Distribution of Last Digit of Jerseys**
**Context:**
A sports company is struggling during the COVID-19 pandemic. The company uses this time for analysis to make profit when the market conditions are favorable. In this case, the company conducted an analysis of the last digit of their jerseys, which were most sold during the FIFA World Cup. They want to test the claim that the last digit of jerseys has the same frequency.
**Data Provided:**
| Last Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|------------|----|----|----|----|----|----|----|----|----|----|
| Frequency | 30 | 35 | 24 | 25 | 35 | 36 | 37 | 27 | 27 | 24 |
**Questions to Answer:**
A) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
B) Find the number of degrees of freedom.
**Explanation:**
A) **Type of Hypothesis Test:**
To determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, we must consider the null hypothesis (H₀) and the alternative hypothesis (H₁).
- **Null Hypothesis (H₀):** The frequencies of the last digit of jerseys are equal.
- **Alternative Hypothesis (H₁):** The frequencies of the last digit of jerseys are not equal.
Since we are interested in testing the equality of frequencies (whether any frequency deviates significantly), we use a **two-tailed test**.
B) **Degrees of Freedom:**
The degrees of freedom (df) for a chi-square test of uniformity can be calculated using the formula:
\[ df = (k - 1) \]
where \( k \) is the number of categories.
In this case, there are 10 categories (the digits 0 to 9):
\[ df = 10 - 1 \]
\[ df = 9 \]
Therefore, the number of degrees of freedom is **9**.
**Summary:**
- The hypothesis test is **two-tailed**.
- The number of degrees of freedom is **9**.](https://content.bartleby.com/qna-images/question/5276d660-6aa9-47cb-b29b-11a8daaff538/7a3e2705-4f16-4213-96ff-80514146d78a/lq0u5lq.jpeg)
Transcribed Image Text:**Hypothesis Testing for Frequency Distribution of Last Digit of Jerseys**
**Context:**
A sports company is struggling during the COVID-19 pandemic. The company uses this time for analysis to make profit when the market conditions are favorable. In this case, the company conducted an analysis of the last digit of their jerseys, which were most sold during the FIFA World Cup. They want to test the claim that the last digit of jerseys has the same frequency.
**Data Provided:**
| Last Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|------------|----|----|----|----|----|----|----|----|----|----|
| Frequency | 30 | 35 | 24 | 25 | 35 | 36 | 37 | 27 | 27 | 24 |
**Questions to Answer:**
A) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
B) Find the number of degrees of freedom.
**Explanation:**
A) **Type of Hypothesis Test:**
To determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, we must consider the null hypothesis (H₀) and the alternative hypothesis (H₁).
- **Null Hypothesis (H₀):** The frequencies of the last digit of jerseys are equal.
- **Alternative Hypothesis (H₁):** The frequencies of the last digit of jerseys are not equal.
Since we are interested in testing the equality of frequencies (whether any frequency deviates significantly), we use a **two-tailed test**.
B) **Degrees of Freedom:**
The degrees of freedom (df) for a chi-square test of uniformity can be calculated using the formula:
\[ df = (k - 1) \]
where \( k \) is the number of categories.
In this case, there are 10 categories (the digits 0 to 9):
\[ df = 10 - 1 \]
\[ df = 9 \]
Therefore, the number of degrees of freedom is **9**.
**Summary:**
- The hypothesis test is **two-tailed**.
- The number of degrees of freedom is **9**.
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